Shedding light on 19th century spectra by analyzing Lippmann photography.

From uncovering the structure of the atom to the nature of the universe, spectral measurements have helped some of science's greatest discoveries. While pointwise spectral measurements date back to Newton, it is commonly thought that hyperspectral images originated in the 1970s. However, the first hyperspectral images are over a century old and are locked in the safes of a handful of museums. These hidden treasures are examples of the first color photographs and earned their inventor, Gabriel Lippmann, the 1908 Nobel Prize in Physics. Since the original work of Lippmann, the process has been predominately understood from the monochromatic perspective, with analogies drawn to Bragg gratings, and the polychromatic case treated as a simple extension. As a consequence, there are misconceptions about the invertibility of the Lippmann process. We show that the multispectral image reflected from a Lippmann plate contains distortions that are not explained by current models. We describe these distortions by directly modeling the process for general spectra and devise an algorithm to recover the original spectra. This results in a complete analysis of the Lippmann process. Finally, we demonstrate the accuracy of our recovery algorithm on self-made Lippmann plates, for which the acquisition setup is fully understood. However, we show that, in the case of historical plates, there are too many unknowns to reliably recover 19th century spectra of natural scenes.

Extension of FRI for modeling of electrocardiogram signals.

Recent work has developed a modeling method applicable to certain types of signals having a "finite rate of innovation" (FRI). Such signals contain a sparse collection of time- or frequency-limited pulses having a restricted set of allowable pulse shapes. A limitation of past work on FRI is that all of the pulses must have the same shape. Many real signals, including electrocardiograms, consist of pulses with varying widths and asymmetry, and therefore are not well fit by the past FRI methods. We present an extension of FRI allowing pulses having variable pulse width (VPW) and asymmetry. We show example results for electrocardiograms and discuss the possibility of application to signal compression and diagnostics.